Determine whether each statement is always, sometimes, or never true. explain your reasoning. (by the way, this has to do with absolute value) and !
a. |x|= |-x|
b. |x|= -|x|
c. |-x|= -|x|

A).  |x| = |-x|
This is always true.
The definition of 'absolute' value is 'size of the number without its sign'.
That's what this expression says.

b).  |x| = -|x|
This is never true, because an absolute value is never negative.
This one would true if x=0 .  So maybe some people might say
it's sometimes true, but that doesn't feel right to me.  I say never.

c).  |-x| = -|x|
This looks to me like exactly the same situation as (b),
and I would say all the same things about it.